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The general pickup and delivery problem
 TRANSPORTATION SCIENCE
, 1995
"... In pickup and delivery problems vehicles have to transport loads from origins to destinations without transshipment atintermediate locations. In this paper, we discuss several characteristics that distinguish them from standard vehicle routing problems and present a survey of the problem types and s ..."
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Cited by 92 (3 self)
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In pickup and delivery problems vehicles have to transport loads from origins to destinations without transshipment atintermediate locations. In this paper, we discuss several characteristics that distinguish them from standard vehicle routing problems and present a survey of the problem types and solution methods found in the literature.
Approximation Algorithms for DeadlineTSP and Vehicle Routing with TimeWindows
 STOC'04
, 2004
"... ..."
Vehicle Routing with Time Windows using Genetic Algorithms
, 1995
"... In vehicle routing problems with time windows (VRPTW), a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for servicing. The objective is to minimize the cost of servicing the set of customers without being ..."
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Cited by 38 (3 self)
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In vehicle routing problems with time windows (VRPTW), a set of vehicles with limits on capacity and travel time are available to service a set of customers with demands and earliest and latest time for servicing. The objective is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. As finding a feasible solution to the problem is NPcomplete, search methods based upon heuristics are most promising for problems of practical size. In this paper we describe GIDEON, a genetic algorithm heuristic for solving the VRPTW. GIDEON consists of a global customer clustering method and a local postoptimization method. The global customer clustering method uses an adaptive search strategy based upon population genetics, to assign vehicles to customers. The best solution obtained from the clustering method is improved by a local postoptimization method. The synergy a between global adaptive clustering method and a local route optimization method produce better results than those obtained by competing heuristic search methods. On a standard set of 56 VRPTW problems obtained from the literature the GIDEON system obtained 41 new best known solutions.
Polyhedral approaches to machine scheduling
, 1996
"... We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition ..."
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Cited by 35 (8 self)
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We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition to those just required for the validity of the initial formulation, in order to obtain useful lower bounds and structural insights. We review formulations based on time–indexed variables; on linear ordering, start time and completion time variables; on assignment and positional date variables; and on traveling salesman variables. We point out relationship between various models, and provide a number of new results, as well as simplified new proofs of known results. In particular, we emphasize the important role that supermodular polyhedra and greedy algorithms play in many formulations and we analyze the strength of the lower and upper bounds obtained from different formulations and relaxations. We discuss separation algorithms for several classes of inequalities, and their potential applicability in generating cutting planes for the practical solution of such scheduling problems. We also review some recent results on approximation algorithms based on some of these formulations.
Hybrid Genetic Algorithm, Simulated Annealing and Tabu Search Methods for Vehicle Routing Problems with Time Windows. Working paper
, 1993
"... The Vehicle Routing Problem with Time Windows (VRPTW) involves servicing a set of customers, with earliest and latest time deadlines, with varying demands using capacitated vehicles with limited travel times. The objective of the problem is to service all customers while minimizing the number of veh ..."
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Cited by 32 (1 self)
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The Vehicle Routing Problem with Time Windows (VRPTW) involves servicing a set of customers, with earliest and latest time deadlines, with varying demands using capacitated vehicles with limited travel times. The objective of the problem is to service all customers while minimizing the number of vehicles and travel distance without violating the capacity and travel time of the vehicles and customer time constraints. In this paper we describe a λinterchange mechanism that moves customers between routes to generate neighborhood solutions for the VRPTW. The λinterchange neighborhood is searched using Simulated Annealing and Tabu Search strategies. The initial solutions to the VRPTW are obtained using the PushForward Insertion heuristic and a Genetic Algorithm based sectoring heuristic. The hybrid combination of the implemented heuristics, collectively known as the GenSAT system, were used to solve 60 problems from the literature with customer sizes varying from 100 to 417 customers. The computational results of GenSAT obtained new best solutions for 40 test problems. For the remaining 20 test problems, 11 solutions obtained by the GenSAT system equal previously known best solutions. The average performance of GenSAT is significantly better than known competing heuristics. For known optimal solutions to the VRPTW problems, the GenSAT system obtained the optimal number of vehicles. Keywords:
Special cases of traveling salesman and repairman problems with time windows
 Networks
, 1992
"... Consider a complete directed graph in which each arc has a given length. There is a set ofjobs, each job i located at some node of the graph, with an associated processing time hi, and whose execution has to start within a prespecified time window [r;, di]. We have a single server that can move on t ..."
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Cited by 29 (0 self)
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Consider a complete directed graph in which each arc has a given length. There is a set ofjobs, each job i located at some node of the graph, with an associated processing time hi, and whose execution has to start within a prespecified time window [r;, di]. We have a single server that can move on the arcs of the graph, at unit speed, and that has to execute all of the jobs within their respective time windows. We consider the following two problems: (a) minimize the time by which all jobs are executed (traveling salesman problem) and (b) minimize the sum of the waiting times of the jobs (traveling repairman problem). We focus on the following two special cases: (a) The jobs are located on a line and (b) the number of nodes of the graph is bounded by some integer constant B. Furthermore, we consider in detail the special cases where (a) all of the processing times are 0, (b) all of the release times ri are 0, and (c) all of the deadlines di are infinite. For many of the resulting problem combinations, we settle their complexity either by establishing NPcompleteness or by presenting polynomial (or pseudopolynomial) time algorithms. Finally, we derive algorithms for the case where, for any time t, the number of jobs that can be executed at that time is bounded. I.
Parallelization of the Vehicle Routing Problem with Time Windows
, 2001
"... Routing with time windows (VRPTW) has been an area of research that have
attracted many researchers within the last 10 { 15 years. In this period a number
of papers and technical reports have been published on the exact solution of the
VRPTW.
The VRPTW is a generalization of the wellknown capacitat ..."
Abstract

Cited by 24 (1 self)
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Routing with time windows (VRPTW) has been an area of research that have
attracted many researchers within the last 10 { 15 years. In this period a number
of papers and technical reports have been published on the exact solution of the
VRPTW.
The VRPTW is a generalization of the wellknown capacitated routing problem
(VRP or CVRP). In the VRP a
eet of vehicles must visit (service) a number
of customers. All vehicles start and end at the depot. For each pair of customers
or customer and depot there is a cost. The cost denotes how much is costs a
vehicle to drive from one customer to another. Every customer must be visited
exactly ones. Additionally each customer demands a certain quantity of goods
delivered (know as the customer demand). For the vehicles we have an upper
limit on the amount of goods that can be carried (known as the capacity). In
the most basic case all vehicles are of the same type and hence have the same
capacity. The problem is now for a given scenario to plan routes for the vehicles
in accordance with the mentioned constraints such that the cost accumulated
on the routes, the xed costs (how much does it cost to maintain a vehicle) or
a combination hereof is minimized.
In the more general VRPTW each customer has a time window, and between
all pairs of customers or a customer and the depot we have a travel time. The
vehicles now have to comply with the additional constraint that servicing of the
customers can only be started within the time windows of the customers. It
is legal to arrive before a time window \opens" but the vehicle must wait and
service will not start until the time window of the customer actually opens.
For solving the problem exactly 4 general types of solution methods have
evolved in the literature: dynamic programming, DantzigWolfe (column generation),
Lagrange decomposition and solving the classical model formulation
directly.
Presently the algorithms that uses DantzigWolfe given the best results
(Desrochers, Desrosiers and Solomon, and Kohl), but the Ph.D. thesis of Kontoravdis
shows promising results for using the classical model formulation directly.
In this Ph.D. project we have used the DantzigWolfe method. In the
DantzigWolfe method the problem is split into two problems: a \master problem"
and a \subproblem". The master problem is a relaxed set partitioning
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problem that guarantees that each customer is visited exactly ones, while the
subproblem is a shortest path problem with additional constraints (capacity and
time window). Using the master problem the reduced costs are computed for
each arc, and these costs are then used in the subproblem in order to generate
routes from the depot and back to the depot again. The best (improving) routes
are then returned to the master problem and entered into the relaxed set partitioning
problem. As the set partitioning problem is relaxed by removing the
integer constraints the solution is seldomly integral therefore the DantzigWolfe
method is embedded in a separationbased solutiontechnique.
In this Ph.D. project we have been trying to exploit structural properties in
order to speed up execution times, and we have been using parallel computers
to be able to solve problems faster or solve larger problems.
The thesis starts with a review of previous work within the eld of VRPTW
both with respect to heuristic solution methods and exact (optimal) methods.
Through a series of experimental tests we seek to dene and examine a number
of structural characteristics.
The rst series of tests examine the use of dividing time windows as the
branching principle in the separationbased solutiontechnique. Instead of using
the methods previously described in the literature for dividing a problem into
smaller problems we use a methods developed for a variant of the VRPTW. The
results are unfortunately not positive.
Instead of dividing a problem into two smaller problems and try to solve
these we can try to get an integer solution without having to branch. A cut is an
inequality that separates the (nonintegral) optimal solution from all the integer
solutions. By nding and inserting cuts we can try to avoid branching. For the
VRPTW Kohl has developed the 2path cuts. In the separationalgorithm for
detecting 2path cuts a number of test are made. By structuring the order in
which we try to generate cuts we achieved very positive results.
In the DantzigWolfe process a large number of columns may be generated,
but a signicant fraction of the columns introduced will not be interesting with
respect to the master problem. It is a priori not possible to determine which
columns are attractive and which are not, but if a column does not become part
of the basis of the relaxed set partitioning problem we consider it to be of no
benet for the solution process. These columns are subsequently removed from
the master problem. Experiments demonstrate a signicant cut of the running
time.
Positive results were also achieved by stopping the routegeneration process
prematurely in the case of timeconsuming shortest path computations. Often
this leads to stopping the shortest path subroutine in cases where the information
(from the dual variables) leads to \bad" routes. The premature exit
from the shortest path subroutine restricts the generation of \bad" routes signi
cantly. This produces very good results and has made it possible to solve
problem instances not solved to optimality before.
The parallel algorithm is based upon the sequential DantzigWolfe based
algorithm developed earlier in the project. In an initial (sequential) phase unsolved
problems are generated and when there are unsolved problems enough
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to start work on every processor the parallel solution phase is initiated. In the
parallel phase each processor runs the sequential algorithm. To get a good workload
a strategy based on balancing the load between neighbouring processors is
implemented. The resulting algorithm is eÆcient and capable of attaining good
speedup values. The loadbalancing strategy shows an even distribution of work
among the processors. Due to the large demand for using the IBM SP2 parallel
computer at UNIC it has unfortunately not be possible to run as many tests
as we would have liked. We have although managed to solve one problem not
solved before using our parallel algorithm.
A reactive variable neighborhood search for the vehicle routing problem with time windows
 INFORMS Journal on Computing
, 2003
"... The purpose of this paper is to present a new deterministic metaheuristic based on a modification of Variable Neighborhood Search of Mladenovic and Hansen (1997) for solving the vehicle routing problem with time windows. Results are reported for the standard 100, 200 and 400 customer data sets by So ..."
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Cited by 21 (0 self)
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The purpose of this paper is to present a new deterministic metaheuristic based on a modification of Variable Neighborhood Search of Mladenovic and Hansen (1997) for solving the vehicle routing problem with time windows. Results are reported for the standard 100, 200 and 400 customer data sets by Solomon (1987) and Gehring and Homberger (1999) and two reallife problems by Russell (1995). The findings indicate that the proposed procedure outperforms other recent local searches and metaheuristics. In addition four new bestknown solutions were obtained. The proposed procedure is based on a new fourphase approach. In this approach an initial solution is first created using new route construction heuristics followed by route elimination procedure to improve the solutions regarding the number of vehicles. In the third phase the solutions are improved in terms of total traveled distance using four new local search procedures proposed in this paper. Finally in phase four the best solution obtained is improved by modifying the objective function to escape from a local minimum. (Metaheuristics; Vehicle Routing; Time Windows) 1.
RealTime Multivehicle Truckload Pickup and Delivery Problems
 Transportation Science
, 2004
"... In this paper we formally introduce a generic realtime multivehicle truckload pickup and delivery problem. The problem includes the consideration of various costs associated with trucks ’ empty travel distances, jobs ’ delayed completion times, and job rejections. Although very simple, the proble ..."
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Cited by 21 (2 self)
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In this paper we formally introduce a generic realtime multivehicle truckload pickup and delivery problem. The problem includes the consideration of various costs associated with trucks ’ empty travel distances, jobs ’ delayed completion times, and job rejections. Although very simple, the problem captures most features of the operational problem of a realworld trucking fleet that dynamically moves truckloads between different sites according to customer requests that arrive continuously over time. We propose a mixed integer programming formulation for the offline version of the problem. We then consider and compare five rolling horizon strategies for the realtime version. Two of the policies are based on a repeated reoptimization of various instances of the offline problem, while the others use simpler local (heuristic) rules. One of the reoptimization strategies is new while the other strategies have recently been tested for similar realtime fleet management problems. The comparison of the policies is done under a general simulation framework. The analysis is systematic and consider varying traffic intensities, varying degrees of advance information, and varying degrees of flexibility for job rejection decisions. The new reoptimization policy is shown to systematically outperform the others under all these conditions.
A Polyhedral Study of the Asymmetric Travelling Salesman Problem with Time Windows
, 1997
"... The asymmetric travelling salesman problem with time windows (ATSPTW) is a basic ..."
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Cited by 14 (3 self)
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The asymmetric travelling salesman problem with time windows (ATSPTW) is a basic